Question

5. You throw a ball straight up from the ground level to a height of 10 ft. The ball falls down and hits the floor. It then bounces back to a height that is 8 ft and repeatedly bouncing up and down indefinitely, each time reaching a height four-fifths of the previous height. (a) When the ball hits the ground the first time, we call this the first hit. Find the height of the ball on the fifth hit. (b) Note that when the ball hits the ground the first time, it has traveled a total vertical distance of 20 ft. Find the total vertical distance the ball has traveled when it hits the ground the fifth time.

Answer 1

Please check out my solution.

solution - h = 10 , hq = 10 (44) hy = 10 (4) 2 , hu = 10/43 'hn = 10/4(n-1) therefore 256 625 &a) hs = 10 (44 hs ² lox > h5 24.096 ft by Total vertical distance till 5th hit 22/10 + 10%) +10()*710133 + 10/304) 2x10 (4)*1) - Total Vertical distance = 67.232 ft (C)') c) Total vertical distance till infinity 2(107 10(9)+ 1°(3)?+ 10( Total vertical distance 2 x 10 = 100 ft)

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